Results 231 to 240 of about 214,123 (281)

Stochastic multisymplectic integrator for stochastic KdV equation

AIP Conference Proceedings, 2012
In this paper we investigate the stochastic multisymplectic methods to solve the stochastic partial differential equation. The stochastic KdV equations are considered. Besides conserving the multi-symplectic structure of original equation, the stochastic multi-symplectic methods are also investigated for the conservation of various conservation laws ...
Shanshan Jiang, Lijin Wang, Jialin Hong
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Stochastic Integrals and Stochastic Differential Equations

1985
Roughly speaking, stochastic differential equations are differential equations driven by Gaussian white noise. Here, we are using the term “stochastic differential equations” in a restricted sense and not merely to denote differential equations with some probabilistic aspects. The importance of.
Eugene Wong, Bruce Hajek
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Abstract stochastic integral equation involving a vector generalized Stochastic integral

Mathematical Notes of the Academy of Sciences of the USSR, 1991
See the review in Zbl 0729.60044.
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Numerical Integration of Stochastic Differential Equations

Bell System Technical Journal, 1979
In a previous paper, a method was presented to integrate numerically nonlinear stochastic differential equations (SDEs) with additive, Gaussian, white noise. The method, a generalization of the Range Kutta algorithm, extrapolates from one point to the next applying functional evaluations at stochastically determined points.
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Manipulating Stochastic Differential Equations and Stochastic Integrals

2015
Many of the calculations of derivative security pricing involve formal manipulations of stochastic differential equations and stochastic integrals. This chapter derives those that are most frequently used. We also consider transformation of correlated Wiener processes to uncorrelated Wiener processes for higher dimensional stochastic differential ...
Carl Chiarella, Xue-Zhong He, Christina Sklibosios Nikitopoulos   +2 more
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Equations for stochastic path integrals

Mathematical Proceedings of the Cambridge Philosophical Society, 1961
Apart from the study of the integralwhere {X(u)} is a stationary Gaussian process with autocorrelation function ρ(t), by Kac and Siegert(1), most stochastic functionals of the general typehave been considered for {X(u)} either additive or Markovian (see, for example, (2), (3)), and in the Markovian case only for diffusion-type processes (Darling and ...
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Langevin equations and stochastic integrals

Zeitschrift f�r Physik B Condensed Matter and Quanta, 1978
The ambiguity of stochastic integrals involved in Langevin equations is removed by the postulate of invariance with respect to nonlinear transformations of the coordinates. The Stratonovich sense of the integrals, which is imposed thereby, is also strongly suggested by stability considerations requiring small changes of the solutions whenever the ...
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Stochastic Integrals and Differential Equations

2004
This chapter provides the tools needed for option pricing. The field of stochastic processes in continuous time, which are defined as solutions of stochastic differential equations, has an important role to play. To illustrate these notions we use repeated approximations by stochastic processes in discrete time and refer to the results from Chapter 4.
Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner   +2 more
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Connections between Stochastic and Ordinary Integral Equations

Advances in Applied Probability, 1980
Let σ: ℝn → M m,n (the space of matrices with m columns and n rows) and b: ℝn → ℝn be two Lipschitz continuousmaps. Suppose that σ is of class C2. Let B = (Bt)t≥0 (B0 = 0) be a standard ℝm valued Brownian motion defined on a probability space (Ω,ƒ, ƒt, P). Consider the solution Xx of the following equation: $$ X_{t}^{X} = x + s.\int_{0}^{t} {\sigma (
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Approximate solution of two dimensional linear and nonlinear stochastic Itô–Volterra integral equations via meshless scheme

Mathematics and Computers in Simulation, 2023
erfan solhi, Farshid Mirzaee
exaly